if f(x) = (4x +3)/(6x - 4), x≠ 2/3 then (f o f)(x)= ?

Question

Mark (√) against the correct answer in the following:

If \(f(x)=\frac{(4x+3)}{(6x-4)},x\neq\frac{2}{3}\) then (f o f) (x) = ?

A. x

B. (2x - 3)

C. \(\frac{4x-6}{3x+4}\)

D. None of these

Answer 1

Correct Answer is (A) x

f(x) = \(\frac{4x-6}{3x+4}\)

\(\Rightarrow f(f(x))=\frac{4f(x)+3}{6f(x)-4}=(fof)(x)\)

\(\Rightarrow f(f(x))=\frac{4(\frac{4x+3}{6x-4})+3}{6(\frac{4x+3}{6x-4})-4}\)

\(\Rightarrow f(f(x))=\frac{16x+12+18x-12}{24x+18-24x+16}\)\(=\frac{34x}{34}\)= x